A059555 Beatty sequence for 1 + gamma A001620.

1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 89, 91, 93, 94, 96, 97, 99, 100, 102, 104, 105, 107, 108

Offset

1,2

Comments

Let r = gamma (the Euler constant, 0.5772...). When {k*r, k >= 1} is jointly ranked with the positive integers, A059555(n) is the position of n and A059556(n) is the position of n*r. - Clark Kimberling, Oct 21 2014

Links

Harry J. Smith, Table of n, a(n) for n = 1..2000

Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no. 4, 335-345.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = n + A038128(n).

Maple

A001620 := proc(n)
        floor((1+gamma)*n) ;
end proc:
seq(A001620(n), n=1..50) ; # R. J. Mathar, Nov 11 2011

Mathematica

t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]
Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]]  (* A059556 *)
Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)
(* Clark Kimberling, Oct 21 2014 *)

Prog

(PARI) { default(realprecision, 100); b=1 + Euler; for (n = 1, 2000, write("b059555.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009
(Magma) R:=RealField(100); [Floor((1+EulerGamma(R))*n): n in [1..100]]; // G. C. Greubel, Aug 27 2018

Crossrefs

Beatty complement is A059556.

Sequence in context: A247779 A243989 A248521 * A186539 A054385 A284773

Adjacent sequences: A059552 A059553 A059554 * A059556 A059557 A059558

Keyword

nonn,easy

Author

Mitch Harris, Jan 22 2001

Status

approved